+ — =¢
x —
MATH THAT MAKES
¢ ENTS
worksheet 3 - Change you can’t count on
GRADE
4
My friend Tonya needed exact change for a juice machine. She only had a $1 bill in her pocket. She
asked if I could trade her $1 in change for her bill.
I knew I had more than $1 in coins in my pocket, so I said, “Sure.” When I emptied my pocket,
however, I found I could not give her exact change for $1.
What is the greatest amount of money in U.S. coins that I can have and still not be able to give
Tonya exact change for $1?
Explain how you know you have found the maximum amount possible.
Extra: Can you find two other combinations of coins that solve the problem?
MATH STANDARDS ALIGNMENT:
Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of
objects, and money, including problems involving simple fractions or decimals, and problems that require expressing
measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams
such as number line diagrams that feature a measurement scale.
Grade 4: Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Construct viable arguments and critique the reasoning of others.
3. Use appropriate tools strategically.
4. Look for and make use of structure.
Personal Finance Big Ideas:
What is Money
METHOD 1: MAXIMIZE QUARTERS:
Since I was trying to find the greatest amount of money, I began with quarters, which are worth the most money. I
couldn’t use four or more, because four quarters would make $1, so I used 3 quarters. Next I thought about dimes. If
I had five or more, I would be able to give Tonya 5 dimes and 2 quarters, making $1, so I knew I couldn’t have more
than 4 dimes. I decided that I must not have any nickels. Just one of them could be combined with 3 quarters and 2
dimes to make $1. I could have 4 pennies, but no more, since that would be like having a nickel.
3 quarters + 4 dimes + 4 pennies = 75¢ + 40¢ + 4¢ = $1.19
[Note: A similar solution may be found starting with a half-dollar, then adding 1 quarter, 4 dimes and 4 pennies.]
1
MATH THAT MAKES CENTS
+ — =¢
x —
MATH THAT MAKES
¢ ENTS
worksheet 3 - Change you can’t count on
GRADE
4
METHOD 2: MAXIMIZE DIMES:
I used real coins to solve the problem. I tried to find the greatest number of dimes without making $1. Nine was the
most I could use. Then I thought about nickels. If I had 2 of them, I’d be able to combine them with the nine dimes and
make $1. If I only had 1 nickel, I would only get to 95¢. To have more than $1 I’d have to have at least 5 pennies, or
some quarters, but then I’d be able to make change for $1. So, I can’t have any nickels. I could add 1 quarter, but no
more, to the 9 dimes without making $1. I could add 4 pennies without being able to make $1 in change.
9 dimes + 1 quarter + 4 pennies = 90¢ + 25¢ + 4¢ = $1.19
Extra: There are three different ways to make $1.19 with current U.S. coins, as described above. A student must list
all three to satisfy the Extra question.
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MATH THAT MAKES CENTS